3.5

ISBN-13:
9780691113852

ISBN-10:
0691113858

Author:
Elias M. Stein, Rami Shakarchi
Publication date:
2003

Publisher:
Princeton University Press

Format:
Hardcover
400 pages
Category:
General

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Book details

ISBN-13:
9780691113852

ISBN-10:
0691113858

Author:
Elias M. Stein, Rami Shakarchi
Publication date:
2003

Publisher:
Princeton University Press

Format:
Hardcover
400 pages
Category:
General

Acknowledged author
Elias M. Stein
wrote Complex Analysis (Princeton Lectures in Analysis, No. 2)
comprising 400 pages back in 2003.
Textbook and eTextbook are published under ISBN 0691113858 and 9780691113852.
Since then Complex Analysis (Princeton Lectures in Analysis, No. 2) textbook
received total rating of 3.5 stars and was available to sell back to BooksRun online for the top buyback price
of $ 27.65 or rent at the marketplace.

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle.

With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory.

Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, *Complex Analysis* will be welcomed by students of mathematics, physics, engineering and other sciences.

The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which *Complex Analysis* is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

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